Given ​ f(x)=x2+14x+40. Enter the quadratic function in vertex form in the box.

For this case we have an equation of the form:
 [tex]y = ax ^ 2 + bx + c [/tex]
 This equation in vertex form is:
 [tex]f (x) = a (x - h) ^ 2 + k [/tex]
 where (h, k) is the vertex of the parabola.
 We have the following function:
 [tex]f (x) = x ^ 2 + 14x + 40 [/tex]
 We look for the vertice.
 For this, we derive the equation:
 [tex]f '(x) = 2x + 14 [/tex]
 We equal zero and clear the value of x:
 [tex]2x + 14 = 0 2x = -14 x = -14/2 x = -7[/tex]
 Substitute the value of x = -7 in the function:
 [tex]f (-7) = (- 7) ^ 2 + 14 * (- 7) +40 f (-7) = -9[/tex]
 Then, the vertice is:
 [tex](h, k) = (-7, -9) [/tex]
 Substituting values we have:
 [tex]f (x) = (x + 7) ^ 2 - 9[/tex]
 Answer:
 The quadratic function in vertex form is:
 [tex]f (x) = (x + 7) ^ 2 - 9[/tex]